How to get a Task that uses SynchronizationContext? And how are SynchronizationContext used anyway?

How can I obtain a Task, that actually runs an action but is dispatched using
SynchronizationContext.Current.Send/Post?

Use special task scheduler:

Task.Factory.StartNew(
    () => {}, // this will use current synchronization context
    CancellationToken.None, 
    TaskCreationOptions.None, 
    TaskScheduler.FromCurrentSynchronizationContext());

And can anyone recommend a good introduction into SynchronizationContext

Look at the article It’s All About the SynchronizationContext by Stephen Cleary.